Systems and methods for lensless image acquisition

ABSTRACT

Image-sensing devices include odd-symmetry gratings that cast interference patterns over a photodetector array. Grating features offer considerable insensitivity to the wavelength of incident light, and also to the manufactured distance between the grating and the photodetector array. Photographs and other image information can be extracted from interference patterns captured by the photodetector array. Efficient extraction algorithms based on Fourier deconvolution introduce barrel distortion, which can be removed by resampling using correction functions. The sensing devices can be made to minimize distortion that results from efficient extraction algorithms based on Fourier deconvolution.

BACKGROUND

A relatively new type of image-sensing device employs an odd-symmetrygrating to project an interference pattern for capture by aphotodetector array. The grating offers considerable insensitivity tothe wavelength of incident light in a wavelength band of interest, andalso to the manufactured distance between the grating and the array. Thegrating produces an interference pattern quite different from thecaptured scene, but that contains sufficient information tomathematically reconstruct the scene or aspects of the scene. Images canthus be captured without a lens, and cameras can be made smaller thanthose that are reliant on lenses and ray-optical focusing. Embodimentsof such image-sensing devices are detailed in U.S. Publication2014/0253781, which is incorporated herein by reference.

Some imaging applications do not require reconstruction of the imagedscene. For example, tracking movement of a point source using anodd-symmetry grating does not require the overall scene bereconstructed. Where image reconstruction is desired, however, themathematical operations used to invert the raw image data can becomputationally cumbersome.

BRIEF DESCRIPTION OF THE DRAWINGS

The detailed description is illustrated by way of example, and not byway of limitation, in the figures of the accompanying drawings and inwhich like reference numerals refer to similar elements and in which:

FIG. 1A is a cut-away view of an imaging device 100 with a binary,phase-antisymmetric grating 105 overlying a photodetector array 110.

FIG. 1B is a plan view of imaging device 100 of FIG. 1A in accordancewith an embodiment in which grating 105 includes spiral features 130 and135 to produce two-dimensional diffraction patterns.

FIG. 2 depicts a test pattern 200 and corresponding interference pattern205 captured by an embodiment of device 100 of FIGS. 1A and 1B.

FIG. 3 depicts device 100 of FIGS. 1A and 1B with four rays 300, 305,310, and 315 illustrating how the impact of Snell's law on device 100produces demagnification that increases with incident angle.

FIG. 4 shows a simulation of distorted image data 400 that results froma raw Fourier-domain reconstruction of interference pattern 205.

FIG. 5 is another cross section of device 100 of FIG. 1A and includingan imaged object 500 emitting a ray with ideal path 505 and actual path510 illustrating the impact of Snell's law.

FIG. 6 is a plot of the distortion in equation (1) for simulations oflight incident an embodiment of device 100.

FIG. 7 depicts a reduced-distortion image 700 derived using linearinterpolation based on the nearest four pixel addresses.

FIG. 8 is a cross section of an imaging system 800 in accordance withone embodiment.

FIG. 9 is a flowchart 900 detailing how an image of test pattern 200 ofFIG. 2 can be captured and resolved using an embodiment of device 100 ofFIGS. 1A and 1B.

FIG. 10 is a cut-away view of an imaging device 1000 with a binary,phase-antisymmetric grating 1005 in accordance with an embodiment inwhich device structures are made to minimize barrel distortion.

FIG. 11 is a cutaway view of device 1000 of FIG. 10 with some featuresomitted and others emphasized to highlight refractive errors associatedwith layers 1012 and 1013.

FIG. 12 is a cutaway view of a device 1200 similar to device 1000 ofFIGS. 10 and 11 with like-identified elements being the same or similar.

FIG. 13 is a cutaway view of a device 1300 similar to device 1000 ofFIGS. 10 and 11 with like-identified elements being the same or similar.

FIG. 14 is a cross section of an imaging system 1400 in accordance withone embodiment.

DETAILED DESCRIPTION

FIG. 1A is a cut-away view of an imaging device 100 with a binary,phase-antisymmetric grating 105 overlying a photodetector array 110,such as a CCD (charge-coupled device), CMOS (complementarymetal-oxide-semiconductor) or (in the case of thermal IR detection) amicrobolometer sensor. Photodetector array 110 includes photoelements111, and may additionally include a lenslet array that concentratesincident photons onto the most sensitive areas of array 110 to increasequantum efficiency. The features of grating 105 offer considerableinsensitivity to the wavelength of incident light in a wavelength bandof interest, and also to the manufactured distance between grating 105and photodetector array 110.

Light in a wavelength band of interest strikes grating 105 from adirection that is normal to the plane 120 of grating 105. (Unlessotherwise stated, the wavelength band of interest is the visiblespectrum. Cameras developed for use in different applications can havedifferent bands of interest, as is well understood by those of skill inthe art.) Grating 105 produces an interference pattern for capture byarray 110. Digital photographs and other image information can then beextracted from the pattern. Device 100 is constructed to produce rawimage data of high fidelity to support efficient algorithms for imageextraction. Efficient extraction algorithms based on Fourierdeconvolution introduce barrel distortion, which can be removed byresampling using correction functions.

Grating 105 is formed by an interface between light-transmissive mediaof different refractive indices, an optical Lanthanum dense flint glasslayer 115 and polycarbonate plastic layer 116 above grating 105 in thisexample. Each of three boundaries of odd symmetry 125 is indicated usinga vertical, dashed line. The lower features 130 of grating 105 inducephase retardations of half of one wavelength (π radians) relative tohigher features 135. Features on either side of each boundary exhibitodd symmetry. With this arrangement, paired features induce respectivephase delays that differ by approximately half a wavelength over thewavelength band of interest (e.g., visible light). Due to dispersion,the difference in the refractive index of the Lanthanum dense flintglass layer 115 and the polycarbonate above grating 105 is an increasingfunction of wavelength, facilitating a wider wavelength band of interestover which the phase delay is approximately π radians. These elementsproduce an interference pattern for capture by array 110.

Device 100 includes an optional opaque layer 117 patterned to include anaperture that encompasses or defines the effective limits of grating105. The aperture windows captured interference patterns, which tends toreduce edge effects that result from subsequent image-recoveryalgorithms. The aperture can also improve angle sensitivity and spuriouslight rejection, which can be advantageous for e.g. motion detection andmeasurement. Opaque layer 117 can be applied directly to a layer forminggrating 105, and may be coplanar or nearly coplanar with grating 105.Other embodiments omit the aperture, or may include an aperture spacedaway from device 100 instead of or in addition to the aperture in layer117.

The example of FIG. 1A assumes light incident the light interface ofdevice 100 is normal to the plane of phase grating 105, in which case,by Huygens' principle, pairs of spherical wave re-radiators equidistantfrom one of the boundaries of odd symmetry 125 cancel each other out dueto the half wavelength phase delay of the radiator on one side of theboundary 125 compared to the other. Thus, light of any wavelength in theband of interest destructively interferes to produce curtains of minimumintensity under boundaries 125. Neither the depth nor the wavelength oflight over a substantial spectrum significantly influences thisdestructive interference. Constructive interference similarly producesfoci of maximum intensity. Both the low and high features 130 and 135admit light, which provides relatively high quantum efficiency relativeto embodiments that selectively block light.

FIG. 1B is a plan view of imaging device 100 of FIG. 1A in accordancewith an embodiment in which grating 105 includes spiral features 130 and135 to produce two-dimensional diffraction patterns. Relatively narrow(wide) segment spacing works better for relatively high (low)frequencies, feature spacing increases along odd-symmetry boundaries(between elevated and recessed grating regions, represented by dark andlight) with distance from the center. Curved boundaries of odd symmetry,defined between the elevated and recessed regions, extend radially fromthe center of the grating to the periphery, radiating out between thedark (elevated) and light (recessed) arms near the center. In someembodiments, the functional form of the curved boundaries approximates alogarithmic spiral. The area of grating 105 can be greater than that ofthe aperture in layer 117 to provide alignment tolerance inmanufacturing.

Although device 100 can include or be used with a focusing element(e.g., a lens), device 100 does not require a focusing element toproduce images. Rather than focusing, as would be done by a traditionalcamera, device 100 captures a diffraction pattern that bears littleresemblance to an imaged scene, but that is nevertheless interpretableby a computer or processor. Grating 105 creates a certain point-spreadfunction (PSF), a multi-armed thin spiral in this example, on the sensorarray for every point of light in the imaged scene. The location of thecenter of the PSF is uniquely determined by the incident angle of lightfrom the point source. Since faraway scenes can be thought of ascollections of point sources of varying intensity, the sensed signalsresemble a convolution of the PSF with the faraway scene. A scene can becomputationally reconstructed from its corresponding interferencepattern if there is a 1:1 map of scenes to sensor readings. In the casewhere the sensed signals are well approximated by a convolution with afixed PSF, the Fourier components of the scene that are recoverable arethe same as the Fourier components of the PSF with sufficient power tobe observable above the noise sources in the system.

FIG. 2 depicts a test pattern 200 and corresponding interference pattern205 captured by an embodiment of device 100 of FIGS. 1A and 1B.Visually, pattern 205 bears little resemblance to pattern 200. Pattern205 nevertheless includes sufficient information to provide an imagethat is geometrically similar to pattern 205.

Device 100 is a linear system, so image extraction can be accomplishedby applying general linear inversion techniques to pattern 205. Suchtechniques multiply sensed data with the regularized pseudoinverse ofthe transformation exhibited by grating 105. However, these generaltechniques are computationally cumbersome, taking O(n⁴) operations andusing O(n⁴) data for an n-by-n pixel array.

General linear algebra techniques fail to make use of the fact that theoptical transform is approximately a convolution of a scene with the PSFof grating 105. If the optical transfer function instead were a simpleconvolution with the PSF, then one could reconstruct scenes using e.g.Fourier-domain regularized deconvolution algorithms. The computationalcomplexity of these Fourier methods is O(n² log(n)) and they requirestorage of a calibration occupying only O(n²) memory for an n-by-n pixelarray. This advantage is offset for device 100 because Fourierdeconvolution introduces significant barrel distortion.

FIG. 3 depicts device 100 of FIGS. 1A and 1B with four rays 300, 305,310, and 315 illustrating how the impact of Snell's law on device 100produces demagnification that increases with incident angle. Theresultant distortion is commonly referred to as “barrel distortion” or“fisheye.” The layer of polycarbonate plastic 116 and other elementsfrom FIGS. 1A and 1B are omitted for ease of illustration.

Due to Snell's law,

${{\sin\;\theta_{r}} = {\frac{n_{i}}{n_{r}}\sin\;\theta_{i}}},$light incident the grating at a certain angle is refracted to propagateat an angle closer to the normal direction. For small angles, such asfor ray 300, sin θ≈θ≈tan θ; this has the effect of demagnifying theimage by a factor

$\frac{n_{i}}{n_{r}}.$For larger incident angles, however, Snell's law imposes greaterrefraction and concomitant demagnification. The effect of thisdistortion is to pull light from greater incident angles (such as thoseat the corners of the field of view) towards the center of array 110 bya greater demagnification factor than for relatively smaller incidentangles (such as those at the sides of the field of view).

FIG. 4 shows a simulation of distorted image data 400 that results froma raw Fourier-domain reconstruction of interference pattern 205. TheFourier-domain inversion algorithm does not account for Snell's lawdistortion, so the reconstructed image data exhibits barrel distortion.One can see features of pattern 200 in data 400, but the reconstructionplainly includes considerable barrel distortion.

FIG. 5 is another cross section of device 100 of FIG. 1A and includingan imaged object 500 emitting a ray with ideal path 505 and actual path510 illustrating the impact of Snell's law. Object 500 is a distanced_(w) from device 100 and displaced from optical axis 515 by a lateraldistance r_(w). An error err represents the displacement of actual path510 from ideal path 505, and these errors over the incident angles ofincident light combine to create the barrel distortion noted previously.

Barrel distortion can be undone computationally by resampling asfollows. The distance r_(s) of the image of object 500 from the opticalaxis on array 110 is given by trigonometry and Snell's law as follows:

$\begin{matrix}{r_{s} = {h\;{\tan\left( {\sin^{- 1}\left( {\frac{n_{i}}{n_{r}}{\sin\left( {\tan^{- 1}\left( \frac{r_{w}}{d_{w}} \right)} \right)}} \right)} \right)}}} & (1)\end{matrix}$A mathematically-equivalent form of equation (1) that does not involvecalls to trigonometric functions is:

$\begin{matrix}{r_{s} = \frac{{hn}_{i}r_{w}}{d_{w}n_{r}\sqrt{1 + \frac{r_{w}^{2}}{d_{w}^{2}}}\sqrt{1 - \frac{n_{i}^{2}r_{w}^{2}}{n_{r}^{2}\left( {d_{w}^{2} + r_{w}^{2}} \right)}}}} & (2)\end{matrix}$

Here h is the grating-sensor separation, n_(i) is the index ofrefraction between the sensor and the light source, and n_(r) is theindex of refraction in the medium between the grating and the sensor.Equation (1) can be used to calculate the location on array 110 whosecenter corresponds to light incident from any angle, making it possibleto construct a distortion-free map of the imaged scene. Distance d_(w)need not be known; distortion-free images are typically defined to bethose where the image is geometrically similar to the object, and thissimilarity will hold for any assumed distance d_(w).

FIG. 6 is a plot 600 of the distortion in (1) for simulations of lightincident an embodiment of device 100. The location in the rawFourier-domain reconstruction corresponding to any object's distancefrom the optical axis (normalized by lateral distance r_(w)) is given bya curve 605. For small eccentricities curve 605 is approximatelystraight, but for larger angles its slope decreases, indicatingincreased demagnification. This curve was computed with n=1.51, h=155microns, and a pixel pitch of 2.5 microns.

A lookup table generated using equation (1), or on-the-fly computationusing equation (1), can be used to sample the distorted raw Fourierreconstruction (e.g., image data 400 of FIG. 4) to yield areduced-distortion image. FIG. 7 depicts one such reduced-distortionimage 700 derived using linear interpolation based on the nearest fourpixel addresses weighted by the real-valued output of equation (1). Asequation (1) rarely returns integral pixel addresses, the sampling canuse e.g. nearest-neighbor or linear interpolation in some embodiments.

FIG. 8 is a cross section of an imaging system 800 in accordance withone embodiment. System 800 is similar to device 100 of FIGS. 1A and 1B,with like-identified elements being the same or similar. System 800differs from device 100 in that array 110 is integrated with ourotherwise coupled to an integrated circuit (IC) device 810 that supportsimage acquisition and processing. In one embodiment, layer 115 isoptical Lanthanum dense flint glass and layer 116 is a polycarbonateplastic. All the components of system 800 can be integrated into thesame device or package.

In one embodiment, layer 116 is a twenty-micron phase-shift layer of aUV-cured plastic with a refractive index of about 1.4; layer 117 is a2,000 Angstrom tungsten film patterned with an aperture 55 microns indiameter; and layer 115 is a 145 micron layer of glass adhered to array110 via a five-micron layer of an optical adhesive (not shown). Array110, in such an embodiment, can be a 200-by-200 pixel array with a pixelpitch of 1.67 microns.

IC 810 includes a processor 815, random-access memory (RAM) 820, andread-only memory (ROM) 825. ROM 825 can store a digital representationof the deconvolution kernel for the PSF of grating 105, along with otherparameters or lookup tables in support of image processing. Processor815 captures digital image data from array 110 and uses that data withthe stored PSF to compute e.g. image data 400 and image 700 of FIGS. 4and 7. Processor 815 uses RAM 820 to read and write data in support ofimage processing. Processor 815 may include SIMD instructions,butterflies accelerating the Cooley-Tukey FFT algorithm in hardware, andother specialized processing elements which aid fast, power-efficientFourier- or spatial-domain deconvolution.

FIG. 9 is a flowchart 900 detailing how an image of test pattern 200 ofFIG. 2 can be captured and resolved using an embodiment of device 100 ofFIGS. 1A and 1B. First, test pattern 200 is presented such that lightfrom pattern 200 is incident device 100 and passes through grating 105(905) to produce interference pattern 205. Photodetector array 110 thensamples pattern 205 (910). The captured pattern 205 may appearunintelligible; however, because grating 105 has sharp features in itspoint-spread function (PSF), pattern 205 contains rich information aboutthe image.

The PSF of grating 105, possibly in combination with the underlyingarray, is known from a prior calibration or high-fidelity simulation.This information is represented by a response 930, a digitalrepresentation of which can be stored within device 100 or elsewhere.Alternatively, the spatial- or Fourier-domain deconvolution kernelneeded to undo the effects of convolving with the PSF may be stored.Sampled pattern 205 is deconvolved using response 930, using e.g.spatial or Fourier deconvolution, to construct barrel-distorted imagedata 400 (940). Finally, distorted image data 400 is resampled (950) toobtain reduced-distortion image 700.

The noise level and operational requirements for the system may not beconstant in time. For instance, with changing light levels whichinfluence the signal to noise level in captured data or operationalrequirements for at times high resolution, and at other times low noiseeach lead to differences in the appropriate deconvolution kernel. Thesechanging requirements can be met by using deconvolution kernels withchanging regularization parameters. For example, a regularizeddeconvolution kernel can be computed as follows:

$k = {\mathcal{F}^{- 1}\left( \frac{{\mathcal{F}({PSF})}^{*}}{{{\mathcal{F}({PSF})}^{2}} + \gamma} \right)}$where γ depends on the degree of noise robustness desired. It may thusbe desirable for a sensor to have access to a spectrum of deconvolutionkernels, with a variety of noise rejection characteristics. In thiscase, a variety of deconvolution kernels can be stored directly inmemory, or can be computed as needed either from interpolation from twoor more stored deconvolution kernels or from the PSF itself, as will beevident to those skilled in the art.

FIG. 10 is a cut-away view of an imaging device 1000 with a binary,phase-antisymmetric grating 1005 in accordance with another embodiment.Device 1000 is similar to device 100 of FIG. 1, with like-identifiedelements being the same or similar. However, device 1000 is modifiedrelative to device 100 to reduce barrel distortion, and thus supportefficient algorithms for image extraction. In particular, a space abovearray 110 reduces barrel distortion.

Grating 1005 is formed by an interface between light-transmissive mediaof different refractive indices, a twenty-micron phase-shift layer 1012of UV-cured plastic and a twenty-micron layer 1013 of thermoplastic withrespective indices n1=1.41 and n2=1.61 in this example. Differentcombinations of indices can be used, and index n2 can be less than indexn1. A space 1014 with refractive index ni separates layer 1013 fromarray 1010.

In this example, space 1014 provides a separation h3 of about 145microns and has a refractive index ni near one to match the refractiveindex ns of the medium through which light travels from objects in animaged scene to device 1000. For example, index ns might be air, inwhich case index ni would be close to one and the medium separatingarray 1010 from the grating might be e.g. a gas or a vacuum. For aquaticor in vivo applications index ni might be closer to that of the fluidenvironment.

FIG. 11 is a cutaway view of device 1000 of FIG. 10 with some featuresomitted and others emphasized to highlight refractive errors associatedwith layers 1012 and 1013. Absent refraction, a ray 1100 entering theface of device 1000 at an incident angle of 45 degrees follows astraight path. Layers 1012 and 1013 create three refractive interfaces,however, so a ray from a point source 1105 entering the face of device1000 the same 45-degrees angle of incidence and intersecting the gratingat the same point as ray 1100 takes a considerably different path.Following Snell's law, and given the indices ns=1.00, n1=1.41, n2=1.61,and ni=1.00, the divergent path through layer 1012 will produce anerror: e1=h1(tan θ₁−tan θ₂) and the divergent path through layer 1013will produce an error: e2=h2(tan θ₁−tan θ₃), where h1 and h2 are thethicknesses of respective layers 1012 and 1013 and the noted anglesθ_(x) are as labeled in FIG. 11. Because indices ns and ni are equal,both parallel rays entering device 1000 will remain parallel throughspace 1014.

Error e1 is proportional to thickness h1, a value that isinconsequential in comparison with the dimensions of imaged scenes. Inthe embodiment of FIG. 11, in which thickness h1 is twenty microns,error e1 is 8.5 microns for rays incident at an angle of 45 degrees. Forcomparison, the diameter of a human hair ranges between about twenty andeighty microns, so error e1 would be expected to distort an image of ahuman by much less than a hair's breadth for light at incident angles ofover 45 degrees.

Error e2 is proportional to thickness h2, which is the same twentymicrons as for thickness h1. Thickness h2 is far from inconsequential,however, as the relevant dimensions are those of array 1010. In thisexample, error e2 is 9.8 microns for rays incident at an angle of 45degrees. Pixel pitch is 1.67 microns, so the offset imposed by error e2translates into an error of about six pixels for light at incidentangles of over 45 degrees. Such an error ease easily observed in theimage data. Error e2 increases with incident angle, leading to barreldistortion.

FIG. 12 is a cutaway view of a device 1200 similar to device 1000 ofFIGS. 10 and 11 with like-identified elements being the same or similar.Device 1200 differs from device 1000 in that the thickness of theunderlying grating layer 1205 is eight microns rather than twenty. As inthe example of FIG. 11, error e2 is proportional to thickness h2.Reducing thickness h2 by sixty percent likewise reduces error e2 bysixty percent, to about 3.9 microns in this example. Pixel pitch is 1.67microns, so the offset imposed by error e2 translates into an error ofbetween two and three pixels for light at 45-degree incident angles.This represents a considerable improvement over the example of FIG. 11.The reduced distortion of the raw image data improves the quality ofimage recovery by computationally efficient deconvolution techniques.

FIG. 13 is a cutaway view of a device 1300 similar to device 1000 ofFIGS. 10 and 11 with like-identified elements being the same or similar.Device 1300 differs from device 1000 in that the upper grating layer1305 is glass with a refractive index n1=1.5 etched to form a phasegrating of the type detailed previously. An error e1 remains as aconsequence of the optical media above the grating, but this error isrelatively inconsequential for the reasons noted above in connectionwith FIG. 11. Error e2 goes to zero, however, as the only optical mediabelow the grating is a space 1014 with a refractive index ni matchingthat of the scene ns. Any barrel distortion is thus due to error e1,which can generally be ignored.

FIG. 14 is a cross section of an imaging system 1400 in accordance withone embodiment. System 1400 is similar to device 1300 of FIG. 13, withlike-identified elements being the same or similar. System 1400 differsfrom device 1300 in that array 1010 is integrated with or otherwisecoupled to an integrated circuit (IC) device 1410 that supports imageacquisition and processing. All the components of system 1400 can beintegrated into the same device or package using microfabricationtechniques well known to those of skill in the art.

IC 1410 includes a processor 1415, random-access memory (RAM) 1420, andread-only memory (ROM) 1425. ROM 1425 can store a digital representationof the PSF of grating 1005 from which a noise-dependent deconvolutionkernel may be computed. ROM 1425 can store a deconvolution kernel forthe PSF along with other parameters or lookup tables in support of imageprocessing. Processor 1415 captures digital image data from array 1010and uses that data with the stored PSF to compute e.g. images and otherimage data. Processor 1415 uses RAM 1420 to read and write data insupport of image processing. Processor 1415 may include SIMDinstructions, butterflies accelerating the Cooley-Tukey FFT algorithm inhardware, and other specialized processing elements which aid fast,power-efficient Fourier- or spatial-domain deconvolution.

The noise level and operational requirements for the system may not beconstant in time. For instance, with changing light levels whichinfluence the signal to noise level in captured data or operationalrequirements for at times high resolution, and at other times low noiseeach lead to differences in the appropriate deconvolution kernel. Thesechanging requirements can be met by using deconvolution kernels withchanging regularization parameters. For example, a regularizeddeconvolution kernel can be computed as follows:

$k = {\mathcal{F}^{- 1}\left( \frac{{\mathcal{F}({PSF})}^{*}}{{{\mathcal{F}({PSF})}^{2}} + \gamma} \right)}$where γ depends on the degree of noise robustness desired. It may thusbe desirable for a sensor to have access to a spectrum of deconvolutionkernels, with a variety of noise rejection characteristics. In thiscase, a variety of deconvolution kernels can be stored directly inmemory, or can be computed as needed either from interpolation from twoor more stored deconvolution kernels or from the PSF itself, as will beevident to those skilled in the art.

While the subject matter has been described in connection with specificembodiments, other embodiments are also envisioned. For example; whileeach grating detailed previously may be used in connection withphotoreceptors to collect incident light, gratings in accordance withthese and other embodiments can be used more generally in imagingdevices that project images using photoelements that admit light; thewavelength band of interest can be broader or narrower than the visiblespectrum, may be wholly or partially outside the visible spectrum, andmay be discontinuous; cameras and gratings detailed herein can beadapted for use in multi-aperture or programmable-aperture applications;and imaging devices that employ other types of gratings can benefit byapplication of methods disclosed herein. Suitable gratings are detailedin U.S. application Ser. No. 14/458,179 to Patrick Gill, David Stork,and Jay Endsley, filed 12 Aug. 2014 and entitled “Patchwork Fresnel ZonePlates for Lensless Imaging,” which is incorporated herein by reference.Other variations will be evident to those of skill in the art.Therefore, the spirit and scope of the appended claims should not belimited to the foregoing description. Only those claims specificallyreciting “means for” or “step for” should be construed in the mannerrequired under the sixth paragraph of 35 U.S.C. § 112.

What is claimed is:
 1. A system for imaging light from a scene in afirst medium of a first refractive index, the system comprising: aphase-shift layer of a second refractive index having a first surface toface the scene and receive the light from the scene and a second surfaceopposite the first surface and including a grating to produce aninterference pattern of a point-spread function for corresponding pointsof the light from the scene, locations of the point-spread functionsdetermined by incident angles of the points of the light from the scene;and a photodetector array spaced from the phase-shift layer opposite thesecond surface, the photodetector array to sample the interferencepattern; wherein the photodetector array is separated from thephase-shift layer by a second medium of the first refractive index. 2.The system of claim 1, wherein the second medium comprises air.
 3. Thesystem of claim 1, further comprising a second phase-shift layer betweenthe grating and the second medium.
 4. The system of claim 1, furthercomprising an opaque layer defining an aperture between the grating andthe photodetector array.
 5. The system of claim 4, wherein the arrayoccupies an array area and the aperture occupies an aperture area lessthan the array area.
 6. The system of claim 1, further comprising memoryto store the point-spread function of the grating.
 7. The system ofclaim 1, further comprising a processor coupled to the photodetectorarray, the processor to deconvolve the sample of the diffraction patternwith the point-spread function of the grating.
 8. The system of claim 7,the processor to deconvolve the sample using Fourier deconvolution. 9.The system of claim 1, each point-spread function having a centeruniquely determined by an incident angle of the corresponding point ofthe light from the scene.
 10. A system for imaging a scene in a firstmedium of a first refractive index, the system comprising: a firstphase-shift layer of a second refractive index having a first surface toface the scene and a second surface opposite the first surface andincluding a grating to produce a diffraction pattern from the scene; aphotodetector array spaced from the first phase-shift layer opposite thesecond surface, the photodetector array to sample the diffractionpattern; wherein the photodetector array is separated from the firstphase-shift layer by a second medium of the first refractive index; anda second phase-shift layer between the grating and the second medium,wherein the second phase-shift layer is of a thickness less than onesixth a separation between the second phase-shift layer and thephotodetector array.
 11. A system for imaging a scene in a first mediumof a first refractive index, the system comprising: a first phase-shiftlayer of a second refractive index having a first surface to face thescene and a second surface opposite the first surface and including agrating to produce a diffraction pattern from the scene; a photodetectorarray spaced from the first phase-shift layer opposite the secondsurface, the photodetector array to sample the diffraction pattern;wherein the photodetector array is separated from the first phase-shiftlayer by a second medium of the first refractive index; and a secondphase-shift layer between the grating and the second medium, wherein thesecond phase-shift layer is of a third refractive index greater than thefirst refractive index.
 12. The system of claim 11, wherein the thirdrefractive index is greater than the second refractive index.
 13. Thesystem of claim 11, wherein the second refractive index is greater thanthe third refractive index.